Three Dimensional Geometry is central in Class 12 and competitive exams because it builds the ability to analyze lines, planes, distances, and angles in 3D using vectors and coordinate methods. Mastery of this chapter strengthens problem-solving in board exams and is heavily used in JEE/NEET for questions on shortest distances, intersection/containment conditions, and plane-line geometry—often with efficient vector cross/dot product techniques.
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Minutes
20
Questions
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Marking
Q1. Find the perpendicular distance from the point to the plane .
Q2. Find the equation of the plane which passes through the point and contains the line of intersection of the planes and .
Q3. The plane is and the line is given by . Find the shortest distance from to the plane and the coordinates of the point on the plane nearest to .
Distance , nearest point
Distance , nearest point
Distance , nearest point
Distance , nearest point
Q4. Find the shortest distance between the skew lines and . Also find the points on and on at which this shortest distance is attained.
Q5. A variable plane with intercepts on the coordinate axes has equation and passes through the fixed point . The triangle formed by its intercepts has centroid . The locus of is:
Q6. Find the perpendicular distance from the point to the plane .
Q7. For which values of does the line
touch the sphere ?
Q8. Find the equation of the plane passing through the point , parallel to the line
and perpendicular to the plane .
Q9. Assertion (A): If a line is perpendicular to a plane , then is perpendicular to every line lying in .
Reason (R): A line is perpendicular to a plane if it is perpendicular to two distinct lines in the plane that intersect at the point of intersection with the given line.
Both A and R are true and R is a correct explanation of A.
Both A and R are true but R is not a correct explanation of A.
A is true but R is false.
A is false but R is true.
Q10. Let
Points and are the pair for which segment is the shortest joining the two skew lines. Find and the length .
Q11. Find the shortest distance from the point to the line .
Q12. The skew lines and are given by and . The shortest distance between and is
Q13. Find the equation of the plane which contains the line and the point .
Q14. Let and . Find the equation(s) of the plane(s) through the line of intersection of and which make an angle of with the plane .
and
and
and
Only one such plane exists:
Q15. Let and . The length of the shortest segment joining and is
...and 5 more challenging questions available in the interactive simulator.